Concept of quantum wave gravitation in the Euclidean model of space and time

Concept of quantum wave gravitation in the Euclidean model of space and time

Článek WoS

The Euclidean Model of Space and Time (EMST) was created as an alternative to the Special Theory of Relativity (STR) and the associated concept of spacetime. This model subsequently proved successful in describing elementary particles of matter and their wave properties in accordance with de Broglie’s hypothesis. The model is based on a four-dimensional Euclidean space with one compactified dimension, thus differing fundamentally from Minkowski’s (pseudo-Euclidean) space of STR. The fundamental contribution of the EMST lies in the integration of relativity and the wave properties of matter into a single theoretical framework. A logical step in the further development of the EMST as a unified physical concept is the formulation of a theory of gravitation. The article contains the foundations, justifications, and basic mathematical derivations of a scalar theory of gravitation, based exclusively on the wave nature of matter. It demonstrates the primary cause of gravitational action of one particle of matter on another, reveals the common origin of inertial and gravitational forces, and derives the Schwarzschild metric. It also shows small deviations from Newton’s and Einstein’s gravitation.

The Euclidean Model of Space and Time (EMST) was created as an alternative to the Special Theory of Relativity (STR) and the associated concept of spacetime. This model subsequently proved successful in describing elementary particles of matter and their wave properties in accordance with de Broglie’s hypothesis. The model is based on a four-dimensional Euclidean space with one compactified dimension, thus differing fundamentally from Minkowski’s (pseudo-Euclidean) space of STR. The fundamental contribution of the EMST lies in the integration of relativity and the wave properties of matter into a single theoretical framework. A logical step in the further development of the EMST as a unified physical concept is the formulation of a theory of gravitation. The article contains the foundations, justifications, and basic mathematical derivations of a scalar theory of gravitation, based exclusively on the wave nature of matter. It demonstrates the primary cause of gravitational action of one particle of matter on another, reveals the common origin of inertial and gravitational forces, and derives the Schwarzschild metric. It also shows small deviations from Newton’s and Einstein’s gravitation.

de Broglie waves, energy conservation, Euclidean metric, redshift, relativity, time dilation, variable speed of light, wave nature of matter

de Broglie waves, energy conservation, Euclidean metric, redshift, relativity, time dilation, variable speed of light, wave nature of matter

Machotka Radovan

19.02.2026

Frontiers Media SA

Frontiers in Physics

14

14 - 2026

Švýcarská konfederace

1

16

16

https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2026.1737947/full